This invention relates to a fuzzy inference unit which makes a fuzzy inference on the basis of uncertain information and knowledge, such as control, pattern recognition, and decision making.
The fuzzy inference is an inference to make a machine perform judgment and processing in a manner similar to a human being on the basis of knowledge containing uncertainty. It can be said to be an inference appropriate for handling qualitative subjectivity.
The fuzzy inference enables you to describe uncertain knowledge such as experience and perception by means of a "fuzzy set" and an "if - then rule" for processing uncertainty numerically. The portion of "if-" is called an antecedent section and the portion of "then-" is called a consequent section. Membership functions of the fuzzy set are used to describe the portions of "-" of the antecedent and consequent sections.
Fuzzy set A is a set characterized by the function .mu..sub.A (membership function) EQU .mu..sub.A :U.fwdarw.[0,1]
in whole set U. The value .mu..sub.A (.epsilon.[0, 1]: Any real value ranging from 1 to 0) represents how much the element u (.epsilon.U) belongs to the fuzzy set A, namely, grade. If the value .mu..sub.A (u) is near 1, it indicates that the grade in which .mu. belongs to the fuzzy set A is high; if the value .mu..sub.A is near 0, it indicates that the grade in which .mu. belongs to the fuzzy set A is low.
FIG. 1 shows an example of a fuzzy set of an antecedent section. The set labels have the following meanings: NB (negative big) means big in the negative direction; NM (negative medium) means medium in the negative direction; NS (negative small) means small in the negative direction; ZO (zero) means about zero; PS (positive small) means small in the positive direction; PM (positive medium) means medium in the positive direction; and PB (positive big) means big in the positive direction. Although various forms of fuzzy set are possible, triangles and trapezoids as shown in FIG. 1 are often used for actual applications. The fuzzy sets represent uncertain or fuzzy words such as "big", "medium", and "small", and are given names called labels, NB, NM, NS, ZO, PS, PM, and PB, corresponding to the words to be represented. A typical application example of the fuzzy inference is fuzzy control.
Since it is difficult to preset the optimum scale of the fluctuation range of an input signal to a fuzzy inference unit, a control test is normally executed several times for setting and changing the membership function scale. For this reason, the circuit must be changed for each trial and error. If the setup scale is not optimum, the following problem arises: If the input range is wide, an output response to an input change is rapid, resulting in excess control; if the input range is narrow, an output response to an input change is slow.
Thus, scaling of antecedent and consequent sections is important for fuzzy control. This scaling refers to how much the input range and output range of the fuzzy inference unit are to be set.
(1) Antecedent section
As shown in FIG. 1, when the input range is small, even if the same value is input, the effect given to fuzzy control differs as compared with the case in which the input range is large. The case of (a) of FIG. 1 corresponds to membership function PS (positive small) in the antecedent section; that of (b) corresponds to PM (positive medium). That is, when viewed from the membership functions, the case of (b) becomes equivalent to a larger input change than (a), and the manipulated variable as a result of fuzzy control is affected.
(2) Consequent section
On the other hand, the discussion in (1) also applies to the output range of the fuzzy inference unit. If the output range is large as in (a) of FIG. 2, the manipulated variable becomes great; if the output range is small as in (b), the manipulated variable becomes small. Thus, the final manipulated variable varies depending on the input range of the fuzzy inference unit.
Then, for fuzzy control, a problem arises as to how much the input range of the antecedent section and the output range of the consequent section are to be set.